I think it would be cool if, as the people in your world develop more of an understanding of the world they live in, the way you interact with game systems changes. Basically, game systems gain new features when you enter a new era.

So for example, economy. Trade starts off in the bronze and classical era flowing naturally, and while you can stop yourself from trading with a certain faction, you don't control who you do trade with, the trade routes just automatically form to the closest city. Then in the Medieval Era, the idea of mercantilism develops. Now you can have direct control over where you send your trade routes. Then in the renaissance era comes capitalism, which opens up the world market, where in addition to using trade routes as a source of money as before, you can negotiate directly for strategic and luxury resources with all the other cultures you are in contact with, like the marketplace in Endless Legend. Then in the modern era comes ideology and economics. Now trade routes have a different effect based on who your allies and rivals are, with trade bonuses from trading with allies, and cultural influence that impacts approval from trade routes to someone with a different government type. There are also economic policies, like preventing inflation which hurts industry but helps money, or free trade, which gives a trade route money bonus but increases cultural influence by rivals, or embargo, which puts pressure on allies to cut off trade routes with someone. That way as the people in your world develop an understanding of economic systems, you the player get more control over economic systems.

You could apply the same to infrastructure, where roads are at first just a byproduct of trade routes, but in the classical era you are able to build roads and bridges manually if you want to, then in the industrial era you can start building megastructures like dams or longer bridges. Or with militaries, starting in the classical era with professional armies you can increase build cost to give them additional xp and training, while starting in the medieval era with military theory you can have new maneuvers available as part of the combat system. Diplomacy would also work well, it could develop from simple nonagression or open border treaties at the start, to alliances and defensive pacts in the medieval era, to full on treaty organizations and political ideologies in the modern era.

Religion has been a matter of much speculation in this forum, including whether it will even be in the game, but one issue people keep bringing up is how much control you should have over your religion. Looking at it historically, prior to organized religion, the majority of pagan belief systems were just a part of life. After the rise of organized religion, religions adoption wasn't something under an empires control; the Romans hated and persecuted Christians and became Christianized anyway; Buddhism's spread was aided by the Gupta empire in India and yet after a resurgence of Hindu beliefs in India, Buddhism held a majority in places like China but not in the region it had started in. However, this is a 4X game about controlling the story of your culture's development, and if religion is included but is purely up to chance it would leave the player as a passenger to a game system they can't control. But if the system for religion evolved as you played, I think that could be an interesting middle ground.

Pagan religion, the equivalent of the pantheon in civ, could be a bonus you chose early in the Bronze Era. Then organized religion would begin in approximately the classical era as part of the random event system, and its spread would be because of religious pressure along roads and trade routes more than missionaries. The bonuses it provides would be based partly on the 8-value political axis of the city where it started, partly on which pantheon bonus you chose. Where it starts and how it spreads is largely up to chance, but you could chose to persecute that religion if you are hoping for a different bonus, although this decreases stability. Then in the medieval era, you are able to adopt a religion, or allow freedom of religion. A relgion can only be adopted if it has spread to one of your cities. Adopting a religion gives you a stronger bonus along with an influence boost in cities following that religion, automatically persecutes other religions, and allows you to build missionaries. Using missionaries successfully by converting other cities is a cheap source of fame and has diplomatic repercussions. Meanwhile, if you have a policy of religious freedom, stability is increased and you get bonuses from all religions in your empire, but you are unable to build missionaries for fame. Then in the renaissance era, you are able to reform your religion by spending influence. This can be cause for war if your neighbor keeps their old religion, and causes a spike in instability, but basically gives you a new religion with a new bonus, and can also be spread by missionaries.

Problems with having game systems evolve include limiting yourself in earlier eras by not letting you do as much, increasing management which slows down the game as it goes on, and making game features dependent on era rather than simply on what technologies you have unlocked. But given that changes in the way people interacted with things like religion, diplomacy, and the economy are part of what defines historical periodization and the idea of having "eras" at all, I think it would make sense to have new features of game systems appear in new eras.

I could definitely see some techs allowing these changes, I think them being optional additions rather than dumping them all on you when you move up an era would make it easier to ease into the changes.

I agree with Dinode, and even more if - as it seems - there is not only a tech tree, but some kinf of cultural tree. Some mechanisms you're talking about might be introduce by tech, and some others by cultural evolutions. It's more accurate, I think, that the game system evolve slowly because of techs, and culturals aspects, rather than thanks to a change of era. Because a change of era doesn't exist in reality: back to 476, nobody said "Well guys, welcome to the Middle-Age !"